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< a accesskey = "H" href = "../index.html" > HOME < / a >
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< / div > < div id = "content" >
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< h1 class = "title" > Effect on the control system of each stages on the vibration of the station< / h1 >
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< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org31edd78" > 1. Effect of all the control systems on the Sample vibrations< / a >
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< ul >
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< li > < a href = "#org1d47683" > 1.1. Experimental Setup< / a > < / li >
< li > < a href = "#orgfcb7154" > 1.2. Load data< / a > < / li >
< li > < a href = "#orgbe65805" > 1.3. Analysis - Time Domain< / a > < / li >
< li > < a href = "#orgdace4d9" > 1.4. Analysis - Frequency Domain< / a >
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< ul >
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< li > < a href = "#orga76176e" > 1.4.1. Vibrations at the sample location< / a > < / li >
< li > < a href = "#org8d92602" > 1.4.2. Vibrations on the marble< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org6f49679" > 1.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org27d5063" > 2. Effect of all the control systems on the Sample vibrations - One stage at a time< / a >
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< ul >
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< li > < a href = "#org5e1d6ca" > 2.1. Experimental Setup< / a > < / li >
< li > < a href = "#orgdbc788c" > 2.2. Load data< / a > < / li >
< li > < a href = "#orgcaa00c9" > 2.3. Voltage to Velocity< / a > < / li >
< li > < a href = "#org6392409" > 2.4. Analysis - Time Domain< / a > < / li >
< li > < a href = "#org4e22262" > 2.5. Analysis - Frequency Domain< / a >
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< ul >
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< li > < a href = "#org88ffac6" > 2.5.1. Vibrations at the sample location< / a > < / li >
< li > < a href = "#org5eddb65" > 2.5.2. Vibrations on the marble< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org60b1ca9" > 2.6. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgd7c39d5" > 3. Effect of the Symetrie Driver< / a >
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< ul >
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< li > < a href = "#org757e668" > 3.1. Experimental Setup< / a > < / li >
< li > < a href = "#org92c9e9b" > 3.2. Load data< / a > < / li >
< li > < a href = "#orgb405d4d" > 3.3. Analysis - Time Domain< / a > < / li >
< li > < a href = "#org486b9fb" > 3.4. Analysis - Frequency Domain< / a >
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< ul >
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< li > < a href = "#orgd488281" > 3.4.1. Vibrations at the sample location< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org680fcdb" > 3.5. Conclusion< / a > < / li >
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< / ul >
< / li >
< / ul >
< / div >
< / div >
< p >
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This file is organized as follow:
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< / p >
< ul class = "org-ul" >
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< li > Section < a href = "#orgc00965d" > 1< / a > :
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< ul class = "org-ul" >
< li > One geophone on the marble and one at the sample location< / li >
< li > Each stage is turned on one by one< / li >
< / ul > < / li >
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< li > Section < a href = "#org06034f4" > 2< / a > :
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< ul class = "org-ul" >
< li > One geophone on the marble and one at the sample location< / li >
< li > Each stage is turned on one at a time< / li >
< / ul > < / li >
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< li > Section < a href = "#org9b94d23" > 3< / a > :
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< ul class = "org-ul" >
< li > We check if the Symetrie driver induces some vibrations when placed on the marble< / li >
< / ul > < / li >
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< / ul >
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< div id = "outline-container-org31edd78" class = "outline-2" >
< h2 id = "org31edd78" > < span class = "section-number-2" > 1< / span > Effect of all the control systems on the Sample vibrations< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
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< a id = "orgc00965d" > < / a >
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< / p >
< div class = "note" >
< p >
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All the files (data and Matlab scripts) are accessible < a href = "data/effect_control_all.zip" > here< / a > .
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< / p >
< / div >
< / div >
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< div id = "outline-container-org1d47683" class = "outline-3" >
< h3 id = "org1d47683" > < span class = "section-number-3" > 1.1< / span > Experimental Setup< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
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< p >
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We here measure the signals of two L22 geophones:
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< / p >
< ul class = "org-ul" >
< li > One is located on top of the Sample platform< / li >
< li > One is located on the marble< / li >
< / ul >
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< p >
The signals are amplified with voltage amplifiers with the following settings:
< / p >
< ul class = "org-ul" >
< li > gain of 60dB< / li >
< li > AC/DC option set on AC< / li >
< li > Low pass filter set at 1kHz< / li >
< / ul >
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< p >
The signal from the top geophone does not go trought the slip-ring.
< / p >
< p >
First, all the control systems are turned ON, then, they are turned one by one.
Each measurement are done during 50s.
< / p >
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< table id = "org109e9c5" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Summary of the measurements and the states of the control systems< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Ty< / th >
< th scope = "col" class = "org-left" > Ry< / th >
< th scope = "col" class = "org-left" > Slip Ring< / th >
< th scope = "col" class = "org-left" > Spindle< / th >
< th scope = "col" class = "org-left" > Hexapod< / th >
< th scope = "col" class = "org-left" > Meas. file< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < code > meas_003.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < code > meas_004.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < code > meas_005.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < code > meas_006.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < code > meas_007.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < code > meas_008.mat< / code > < / td >
< / tr >
< / tbody >
< / table >
< p >
Each of the < code > mat< / code > file contains one array < code > data< / code > with 3 columns:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column number< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Geophone - Marble< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Geophone - Sample< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
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< div id = "outline-container-orgfcb7154" class = "outline-3" >
< h3 id = "orgfcb7154" > < span class = "section-number-3" > 1.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
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< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > d3 = load('mat/data_003.mat', 'data'); d3 = d3.data;
d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
d6 = load('mat/data_006.mat', 'data'); d6 = d6.data;
d7 = load('mat/data_007.mat', 'data'); d7 = d7.data;
d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgbe65805" class = "outline-3" >
< h3 id = "orgbe65805" > < span class = "section-number-3" > 1.3< / span > Analysis - Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
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< p >
First, we can look at the time domain data and compare all the measurements:
< / p >
< ul class = "org-ul" >
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< li > comparison for the geophone at the sample location (figure < a href = "#org1e12b9d" > 1< / a > )< / li >
< li > comparison for the geophone on the granite (figure < a href = "#orga090daf" > 2< / a > )< / li >
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< / ul >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(d3(:, 3), d3(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Hexa, Rz, SR');
plot(d6(:, 3), d6(:, 2), 'DisplayName', 'Hexa, Rz');
plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Hexa');
plot(d8(:, 3), d8(:, 2), 'DisplayName', 'All OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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< / pre >
< / div >
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< div id = "org1e12b9d" class = "figure" >
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< p > < img src = "figs/time_domain_sample.png" alt = "time_domain_sample.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 1: < / span > Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location< / p >
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< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(d3(:, 3), d3(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Hexa, Rz, SR');
plot(d6(:, 3), d6(:, 1), 'DisplayName', 'Hexa, Rz');
plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Hexa');
plot(d8(:, 3), d8(:, 1), 'DisplayName', 'All OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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< / pre >
< / div >
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< div id = "orga090daf" class = "figure" >
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< p > < img src = "figs/time_domain_marble.png" alt = "time_domain_marble.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 2: < / span > Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgdace4d9" class = "outline-3" >
< h3 id = "orgdace4d9" > < span class = "section-number-3" > 1.4< / span > Analysis - Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-1-4" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = d3(2, 3) - d3(1, 3);
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Fs = 1/dt;
win = hanning(ceil(10*Fs));
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< / pre >
< / div >
< / div >
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< div id = "outline-container-orga76176e" class = "outline-4" >
< h4 id = "orga76176e" > < span class = "section-number-4" > 1.4.1< / span > Vibrations at the sample location< / h4 >
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< div class = "outline-text-4" id = "text-1-4-1" >
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< p >
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [px3, f] = pwelch(d3(:, 2), win, [], [], Fs);
[px4, ~] = pwelch(d4(:, 2), win, [], [], Fs);
[px5, ~] = pwelch(d5(:, 2), win, [], [], Fs);
[px6, ~] = pwelch(d6(:, 2), win, [], [], Fs);
[px7, ~] = pwelch(d7(:, 2), win, [], [], Fs);
[px8, ~] = pwelch(d8(:, 2), win, [], [], Fs);
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< / pre >
< / div >
< p >
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And we compare all the signals (figures < a href = "#orgc7cf107" > 3< / a > and < a href = "#org2cc793f" > 4< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(px7), 'DisplayName', 'Hexa');
plot(f, sqrt(px8), 'DisplayName', 'All OFF');
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hold off;
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set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'southwest');
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< / pre >
< / div >
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< div id = "orgc7cf107" class = "figure" >
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< p > < img src = "figs/psd_sample_comp.png" alt = "psd_sample_comp.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 3: < / span > Amplitude Spectral Density of the signal coming from the top geophone< / p >
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< / div >
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< div id = "org2cc793f" class = "figure" >
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< p > < img src = "figs/psd_sample_comp_high_freq.png" alt = "psd_sample_comp_high_freq.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 4: < / span > Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org8d92602" class = "outline-4" >
< h4 id = "org8d92602" > < span class = "section-number-4" > 1.4.2< / span > Vibrations on the marble< / h4 >
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< div class = "outline-text-4" id = "text-1-4-2" >
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< p >
Now we plot the same curves for the geophone located on the marble.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [px3, f] = pwelch(d3(:, 1), win, [], [], Fs);
[px4, ~] = pwelch(d4(:, 1), win, [], [], Fs);
[px5, ~] = pwelch(d5(:, 1), win, [], [], Fs);
[px6, ~] = pwelch(d6(:, 1), win, [], [], Fs);
[px7, ~] = pwelch(d7(:, 1), win, [], [], Fs);
[px8, ~] = pwelch(d8(:, 1), win, [], [], Fs);
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< / pre >
< / div >
< p >
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And we compare the Amplitude Spectral Densities (figures < a href = "#org60f624e" > 5< / a > and < a href = "#org9480bcc" > 6< / a > )
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(px7), 'DisplayName', 'Hexa');
plot(f, sqrt(px8), 'DisplayName', 'All OFF');
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hold off;
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set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'northeast');
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< / pre >
< / div >
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< div id = "org60f624e" class = "figure" >
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< p > < img src = "figs/psd_marble_comp.png" alt = "psd_marble_comp.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 5: < / span > Amplitude Spectral Density of the signal coming from the top geophone< / p >
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< / div >
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< div id = "org9480bcc" class = "figure" >
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< p > < img src = "figs/psd_marble_comp_high_freq.png" alt = "psd_marble_comp_high_freq.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 6: < / span > Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org6f49679" class = "outline-3" >
< h3 id = "org6f49679" > < span class = "section-number-3" > 1.5< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-1-5" >
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< div class = "important" >
< ul class = "org-ul" >
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< li > The control system of the Ty stage induces a lot of vibrations of the marble above 100Hz< / li >
< li > The hexapod control system add vibrations of the sample only above 200Hz< / li >
< li > When the Slip-Ring is ON, white noise appears at high frequencies. This is studied < a href = "../slip-ring-electrical-noise/index.html" > here< / a > < / li >
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< / ul >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org27d5063" class = "outline-2" >
< h2 id = "org27d5063" > < span class = "section-number-2" > 2< / span > Effect of all the control systems on the Sample vibrations - One stage at a time< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< p >
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< a id = "org06034f4" > < / a >
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< / p >
< div class = "note" >
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/effect_control_one.zip" > here< / a > .
< / p >
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< / div >
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< / div >
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< div id = "outline-container-org5e1d6ca" class = "outline-3" >
< h3 id = "org5e1d6ca" > < span class = "section-number-3" > 2.1< / span > Experimental Setup< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
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< p >
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We here measure the signals of two geophones:
< / p >
< ul class = "org-ul" >
< li > One is located on top of the Sample platform< / li >
< li > One is located on the marble< / li >
< / ul >
< p >
The signal from the top geophone does go trought the slip-ring.
< / p >
< p >
All the control systems are turned OFF, then, they are turned on one at a time.
< / p >
< p >
Each measurement are done during 100s.
< / p >
< p >
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The settings of the voltage amplifier are shown on figure < a href = "#org8b2d864" > 7< / a > :
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< / p >
< ul class = "org-ul" >
< li > gain of 60dB< / li >
< li > AC/DC option set on DC< / li >
< li > Low pass filter set at 1kHz< / li >
< / ul >
< p >
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A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
< / p >
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< table id = "org71b8a99" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 2:< / span > Summary of the measurements and the states of the control systems< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Ty< / th >
< th scope = "col" class = "org-left" > Ry< / th >
< th scope = "col" class = "org-left" > Slip Ring< / th >
< th scope = "col" class = "org-left" > Spindle< / th >
< th scope = "col" class = "org-left" > Hexapod< / th >
< th scope = "col" class = "org-left" > Meas. file< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < code > meas_013.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < code > meas_014.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < code > meas_015.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < code > meas_016.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < code > meas_017.mat< / code > < / td >
< / tr >
< tr >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < code > meas_018.mat< / code > < / td >
< / tr >
< / tbody >
< / table >
< p >
Each of the < code > mat< / code > file contains one array < code > data< / code > with 3 columns:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column number< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Geophone - Marble< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Geophone - Sample< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
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< div id = "org8b2d864" class = "figure" >
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< p > < img src = "./img/IMG_20190507_101459.jpg" alt = "IMG_20190507_101459.jpg" width = "500px" / >
< / p >
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< p > < span class = "figure-number" > Figure 7: < / span > Voltage amplifier settings for the measurement< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgdbc788c" class = "outline-3" >
< h3 id = "orgdbc788c" > < span class = "section-number-3" > 2.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
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< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > d_of = load('mat/data_013.mat', 'data'); d_of = d_of.data;
d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data;
d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data;
d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data;
d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data;
d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgcaa00c9" class = "outline-3" >
< h3 id = "orgcaa00c9" > < span class = "section-number-3" > 2.3< / span > Voltage to Velocity< / h3 >
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< div class = "outline-text-3" id = "text-2-3" >
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< p >
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We convert the measured voltage to velocity using the function < code > voltageToVelocityL22< / code > (accessible < a href = "file:///home/thomas/Cloud/thesis/meas/srcindex.html" > here< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > gain = 60; % [dB]
d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain);
d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain);
d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain);
d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain);
d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain);
d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain);
d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain);
d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain);
d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain);
d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain);
d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain);
d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org6392409" class = "outline-3" >
< h3 id = "org6392409" > < span class = "section-number-3" > 2.4< / span > Analysis - Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-2-4" >
< p >
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First, we can look at the time domain data and compare all the measurements:
< / p >
< ul class = "org-ul" >
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< li > comparison for the geophone at the sample location (figure < a href = "#org6b5b92c" > 8< / a > )< / li >
< li > comparison for the geophone on the granite (figure < a href = "#org90b0f48" > 9< / a > )< / li >
< li > relative displacement of the sample with respect to the marble (figure < a href = "#org90b0f48" > 9< / a > )< / li >
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< / ul >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
plot(d_ty(:, 3), d_ty(:, 2), 'DisplayName', 'Ty ON');
plot(d_ry(:, 3), d_ry(:, 2), 'DisplayName', 'Ry ON');
plot(d_sr(:, 3), d_sr(:, 2), 'DisplayName', 'S-R ON');
plot(d_rz(:, 3), d_rz(:, 2), 'DisplayName', 'Rz ON');
plot(d_he(:, 3), d_he(:, 2), 'DisplayName', 'Hexa ON');
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hold off;
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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< / pre >
< / div >
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< div id = "org6b5b92c" class = "figure" >
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< p > < img src = "figs/time_domain_sample_lpf.png" alt = "time_domain_sample_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 8: < / span > Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location< / p >
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< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
plot(d_ty(:, 3), d_ty(:, 1), 'DisplayName', 'Ty ON');
plot(d_ry(:, 3), d_ry(:, 1), 'DisplayName', 'Ry ON');
plot(d_sr(:, 3), d_sr(:, 1), 'DisplayName', 'S-R ON');
plot(d_rz(:, 3), d_rz(:, 1), 'DisplayName', 'Rz ON');
plot(d_he(:, 3), d_he(:, 1), 'DisplayName', 'Hexa ON');
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hold off;
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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< / pre >
< / div >
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< div id = "org90b0f48" class = "figure" >
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< p > < img src = "figs/time_domain_marble_lpf.png" alt = "time_domain_marble_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 9: < / span > Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble< / p >
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< / div >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(d_of(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_of(:, 2)-d_of(:, 1), d_of(:, 3)), 'DisplayName', 'All OFF');
plot(d_ty(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ty(:, 2)-d_ty(:, 1), d_ty(:, 3)), 'DisplayName', 'Ty ON');
plot(d_ry(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ry(:, 2)-d_ry(:, 1), d_ry(:, 3)), 'DisplayName', 'Ry ON');
plot(d_sr(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_sr(:, 2)-d_sr(:, 1), d_sr(:, 3)), 'DisplayName', 'S-R ON');
plot(d_rz(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_rz(:, 2)-d_rz(:, 1), d_rz(:, 3)), 'DisplayName', 'Rz ON');
plot(d_he(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_he(:, 2)-d_he(:, 1), d_he(:, 3)), 'DisplayName', 'Hexa ON');
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hold off;
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xlabel('Time [s]'); ylabel('Relative Displacement [$\mu m$]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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< / pre >
< / div >
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< div id = "org5d1a458" class = "figure" >
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< p > < img src = "figs/time_domain_relative_disp.png" alt = "time_domain_relative_disp.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 10: < / span > Relative displacement of the sample with respect to the marble< / p >
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< / div >
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< / div >
< / div >
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< div id = "outline-container-org4e22262" class = "outline-3" >
< h3 id = "org4e22262" > < span class = "section-number-3" > 2.5< / span > Analysis - Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-2-5" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = d_of(2, 3) - d_of(1, 3);
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Fs = 1/dt;
win = hanning(ceil(10*Fs));
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< / pre >
< / div >
< / div >
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< div id = "outline-container-org88ffac6" class = "outline-4" >
< h4 id = "org88ffac6" > < span class = "section-number-4" > 2.5.1< / span > Vibrations at the sample location< / h4 >
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< div class = "outline-text-4" id = "text-2-5-1" >
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< p >
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [px_of, f] = pwelch(d_of(:, 2), win, [], [], Fs);
[px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs);
[px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs);
[px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs);
[px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs);
[px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs);
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< / pre >
< / div >
< p >
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And we compare all the signals (figures < a href = "#org184f693" > 11< / a > and < a href = "#orgc76db7e" > 12< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
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hold off;
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set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'southwest');
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< / pre >
< / div >
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< div id = "org184f693" class = "figure" >
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< p > < img src = "figs/psd_sample_comp_lpf.png" alt = "psd_sample_comp_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 11: < / span > Amplitude Spectral Density of the sample velocity< / p >
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< / div >
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< div id = "orgc76db7e" class = "figure" >
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< p > < img src = "figs/psd_sample_comp_high_freq_lpf.png" alt = "psd_sample_comp_high_freq_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 12: < / span > Amplitude Spectral Density of the sample velocity (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org5eddb65" class = "outline-4" >
< h4 id = "org5eddb65" > < span class = "section-number-4" > 2.5.2< / span > Vibrations on the marble< / h4 >
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< div class = "outline-text-4" id = "text-2-5-2" >
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< p >
Now we plot the same curves for the geophone located on the marble.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [px_of, f] = pwelch(d_of(:, 1), win, [], [], Fs);
[px_ty, ~] = pwelch(d_ty(:, 1), win, [], [], Fs);
[px_ry, ~] = pwelch(d_ry(:, 1), win, [], [], Fs);
[px_sr, ~] = pwelch(d_sr(:, 1), win, [], [], Fs);
[px_rz, ~] = pwelch(d_rz(:, 1), win, [], [], Fs);
[px_he, ~] = pwelch(d_he(:, 1), win, [], [], Fs);
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< / pre >
< / div >
< p >
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And we compare the Amplitude Spectral Densities (figures < a href = "#org8c00376" > 13< / a > and < a href = "#org1008de7" > 14< / a > )
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
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hold off;
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set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'northeast');
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< / pre >
< / div >
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< div id = "org8c00376" class = "figure" >
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< p > < img src = "figs/psd_marble_comp_lpf.png" alt = "psd_marble_comp_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 13: < / span > Amplitude Spectral Density of the marble velocity< / p >
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< / div >
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< div id = "org1008de7" class = "figure" >
< p > < img src = "figs/psd_marble_lpf_high_freq.png" alt = "psd_marble_lpf_high_freq.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 14: < / span > Amplitude Spectral Density of the marble velocity (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org60b1ca9" class = "outline-3" >
< h3 id = "org60b1ca9" > < span class = "section-number-3" > 2.6< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-2-6" >
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< div class = "important" >
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< ul class = "org-ul" >
< li > The Ty stage induces vibrations of the marble and at the sample location above 100Hz< / li >
< li > The hexapod stage induces vibrations at the sample position above 220Hz< / li >
< / ul >
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< / div >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgd7c39d5" class = "outline-2" >
< h2 id = "orgd7c39d5" > < span class = "section-number-2" > 3< / span > Effect of the Symetrie Driver< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< p >
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< a id = "org9b94d23" > < / a >
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< / p >
< div class = "note" >
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/effect_symetrie_driver.zip" > here< / a > .
< / p >
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< / div >
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< / div >
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< div id = "outline-container-org757e668" class = "outline-3" >
< h3 id = "org757e668" > < span class = "section-number-3" > 3.1< / span > Experimental Setup< / h3 >
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< div class = "outline-text-3" id = "text-3-1" >
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< p >
We here measure the signals of two geophones:
< / p >
< ul class = "org-ul" >
< li > One is located on top of the Sample platform< / li >
< li > One is located on the marble< / li >
< / ul >
< p >
The signal from the top geophone does go trought the slip-ring.
< / p >
< p >
All the control systems are turned OFF except the Hexapod one.
< / p >
< p >
Each measurement are done during 100s.
< / p >
< p >
The settings of the voltage amplifier are:
< / p >
< ul class = "org-ul" >
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< li > gain of 60dB< / li >
< li > AC/DC option set on DC< / li >
< li > Low pass filter set at 1kHz< / li >
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< / ul >
< p >
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
< / p >
< p >
The measurements are:
< / p >
< ul class = "org-ul" >
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< li > < code > meas_018.mat< / code > : Hexapod’ s driver on the granite< / li >
< li > < code > meas_019.mat< / code > : Hexapod’ s driver on the ground< / li >
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< / ul >
< p >
Each of the < code > mat< / code > file contains one array < code > data< / code > with 3 columns:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column number< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Geophone - Marble< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Geophone - Sample< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
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< div id = "outline-container-org92c9e9b" class = "outline-3" >
< h3 id = "org92c9e9b" > < span class = "section-number-3" > 3.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-3-2" >
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< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > d_18 = load('mat/data_018.mat', 'data'); d_18 = d_18.data;
d_19 = load('mat/data_019.mat', 'data'); d_19 = d_19.data;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgb405d4d" class = "outline-3" >
< h3 id = "orgb405d4d" > < span class = "section-number-3" > 3.3< / span > Analysis - Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-3-3" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(d_19(:, 3), d_19(:, 1), 'DisplayName', 'Driver - Ground');
plot(d_18(:, 3), d_18(:, 1), 'DisplayName', 'Driver - Granite');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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< / pre >
< / div >
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< div id = "org33aab52" class = "figure" >
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< p > < img src = "figs/time_domain_hexa_driver.png" alt = "time_domain_hexa_driver.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 15: < / span > Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org486b9fb" class = "outline-3" >
< h3 id = "org486b9fb" > < span class = "section-number-3" > 3.4< / span > Analysis - Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-3-4" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = d_18(2, 3) - d_18(1, 3);
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Fs = 1/dt;
win = hanning(ceil(10*Fs));
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< / pre >
< / div >
< / div >
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< div id = "outline-container-orgd488281" class = "outline-4" >
< h4 id = "orgd488281" > < span class = "section-number-4" > 3.4.1< / span > Vibrations at the sample location< / h4 >
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< div class = "outline-text-4" id = "text-3-4-1" >
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< p >
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [px_18, f] = pwelch(d_18(:, 1), win, [], [], Fs);
[px_19, ~] = pwelch(d_19(:, 1), win, [], [], Fs);
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > figure;
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hold on;
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plot(f, sqrt(px_19), 'DisplayName', 'Driver - Ground');
plot(f, sqrt(px_18), 'DisplayName', 'Driver - Granite');
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hold off;
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set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'southwest');
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< / pre >
< / div >
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< div id = "org23ad3aa" class = "figure" >
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< p > < img src = "figs/psd_hexa_driver.png" alt = "psd_hexa_driver.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 16: < / span > Amplitude Spectral Density of the signal coming from the top geophone< / p >
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< / div >
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< div id = "org0b027ce" class = "figure" >
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< p > < img src = "figs/psd_hexa_driver_high_freq.png" alt = "psd_hexa_driver_high_freq.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 17: < / span > Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org680fcdb" class = "outline-3" >
< h3 id = "org680fcdb" > < span class = "section-number-3" > 3.5< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-3-5" >
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< div class = "important" >
< p >
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Even tough the Hexapod’ s driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground.
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< / p >
< / div >
< / div >
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< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
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< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2020-04-23 jeu. 15:28< / p >
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< / div >
< / body >
< / html >
